π there, you are no guilty of intellectual property theft, possession of classified information, and possession of child pornography. Please report to your nearest prison.

Someone actually made a pi-based filesystem for Linux. Rather than storing the actual data on disk, it only stores the file's length and earliest position in the digits of pi. This saves a hell of a lot of space on disk, at the cost of some "minor performance problems."

Not all "infinite non repeating," i.e. irrational, numbers include every finite sequence of digits. For example, 1.H1^H001.... is irrational - there's not a repeating pattern, but it misses a lot of strings of digits. Pi may or may not include all sequences of digits - it hasn't been proven either way.

Not all "infinite non repeating," i.e. irrational, numbers include every finite sequence of digits. For example, 1.H1^H001.... is irrational - there's not a repeating pattern, but it misses a lot of strings of digits. Pi may or may not include all sequences of digits - it hasn't been proven either way.

html ate my number - it should be 1.H1^H001.... (the string of 0s between 1s gets longer each time.)

Not all "infinite non repeating," i.e. irrational, numbers include every finite sequence of digits. For example, 1.H1^H001.... is irrational - there's not a repeating pattern, but it misses a lot of strings of digits. Pi may or may not include all sequences of digits - it hasn't been proven either way.

html ate my number - it should be 1.H1^H001.... (the string of 0s between 1s gets longer each time.)

Not all "infinite non repeating," i.e. irrational, numbers include every finite sequence of digits. For example, 1.H1^H001.... is irrational - there's not a repeating pattern, but it misses a lot of strings of digits. Pi may or may not include all sequences of digits - it hasn't been proven either way.

html ate my number - it should be 1.H1^H001.... (the string of 0s between 1s gets longer each time.)

Not all "infinite non repeating," i.e. irrational, numbers include every finite sequence of digits. For example, 1.H1^H001.... is irrational - there's not a repeating pattern, but it misses a lot of strings of digits. Pi may or may not include all sequences of digits - it hasn't been proven either way.

You don't necessarily need to prove that it contains all possible sequences of digits of any length. For example, if you can demonstrate that it contains every possible sequence from 0 through 255, then you could build every possible file from a list of bytes.

That's how the current implementation of that pi-based filesystem I was talking about works, "to maximize performance." I'm fairly sure that this particular implementation doesn't actually wind up saving any disk space, despite my claims above. But if you were willing to accept the above "minor performance problems", which even the current implementation still has, you could do it.

Not all "infinite non repeating," i.e. irrational, numbers include every finite sequence of digits. For example, 1.H1^H001.... is irrational - there's not a repeating pattern, but it misses a lot of strings of digits. Pi may or may not include all sequences of digits - it hasn't been proven either way.

html ate my number - it should be 1.H1^H001.... (the string of 0s between 1s gets longer each time.)

Every additional decimal point you find of pi makes it become a larger number, but pi as a concept is always the same number. But pi as a concept is infinitely long, so it's always infinitely larger than what we think. (???)

Foxxinnia:Every additional decimal point you find of pi makes it become a larger number, but pi as a concept is always the same number. But pi as a concept is infinitely long, so it's always infinitely larger than what we think. (???)

Uh... trolling or actually not clear on this point? Pi is always exactly the same value, and actually there are formulas for calculating any digit of it, so it always remains constant. There's nothing we have left to "discover". We don't "think" it's 3.1416, we just use that as a good-enough approximation. What you said is like telling someone that as you open a door to a house, the house you're entering gets bigger because you're seeing more of it.

Millennium:Someone actually made a pi-based filesystem for Linux. Rather than storing the actual data on disk, it only stores the file's length and earliest position in the digits of pi. This saves a hell of a lot of space on disk, at the cost of some "minor performance problems."

Arkanaut:Foxxinnia: Every additional decimal point you find of pi makes it become a larger number, but pi as a concept is always the same number. But pi as a concept is infinitely long, so it's always infinitely larger than what we think. (???)

Uh... trolling or actually not clear on this point? Pi is always exactly the same value, and actually there are formulas for calculating any digit of it, so it always remains constant. There's nothing we have left to "discover". We don't "think" it's 3.1416, we just use that as a good-enough approximation. What you said is like telling someone that as you open a door to a house, the house you're entering gets bigger because you're seeing more of it.

I think what he's saying is that 3.14 is less than 3.141, so that every time you add a digit it gets slightly bigger. It's one of those things where you don't even know where to start...convergent series or just plain "this is how you round".

Millennium:Rather than storing the actual data on disk, it only stores the file's length and earliest position in the digits of pi. This saves a hell of a lot of space on disk, at the cost of some "minor performance problems."

Not really. Let's suppose for the moment that pi is actually "normal" in base-2: that is contains all finite strings at the "expected" frequency. Roughly speaking: the bit sequence of pi is 'random'.

Now, consider an arbitrary string (or 'file') of length N bits. As there are 2^N strings of this length, we would expect to find this arbitrary string inside pi after around 2^N binary places. Some length-N strings would, of course, appear before, and others after. But on average we would expect to wait 2^N bits.

So when the encoding of a string is (N, p), where p is the position of the string inside pi, we would expect p to be of size 2^N on average. Such a number takes N bits to store (in our pi-filesystem). But the file itself is N bits long, so we haven't saved any space.

It is impossible to come up with a compression scheme that can compress *all* files. This is easy to see. There are 2^N binary strings of length N, but only 2^N -1 strings of length less than N.

StrangeQ:Arkanaut: Foxxinnia: Every additional decimal point you find of pi makes it become a larger number, but pi as a concept is always the same number. But pi as a concept is infinitely long, so it's always infinitely larger than what we think. (???)

Uh... trolling or actually not clear on this point? Pi is always exactly the same value, and actually there are formulas for calculating any digit of it, so it always remains constant. There's nothing we have left to "discover". We don't "think" it's 3.1416, we just use that as a good-enough approximation. What you said is like telling someone that as you open a door to a house, the house you're entering gets bigger because you're seeing more of it.

I think what he's saying is that 3.14 is less than 3.141, so that every time you add a digit it gets slightly bigger. It's one of those things where you don't even know where to start...convergent series or just plain "this is how you round".